Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_pH 36 2.248838
beta0_pH 36 2.049604
beta1_pH 38 1.693602
beta0_yellow 9 1.677351
beta1_yellow 11 1.601363
beta2_pH 31 1.587275
beta3_yellow 9 1.525085
mu_beta0_pH 8 1.522730
beta1_pelagic 12 1.483799
beta0_pelagic 7 1.447417
beta3_pelagic 10 1.424249
parameter n badRhat_avg
beta2_pelagic 10 1.376453
tau_beta0_yellow 2 1.336729
tau_beta0_pH 8 1.326694
beta2_black 5 1.296956
beta2_yellow 5 1.274411
beta1_black 10 1.259834
beta_H 10 1.239194
tau_beta0_black 1 1.206832
tau_beta0_pelagic 1 1.165714
beta3_black 1 1.144851
beta0_black 1 1.132095
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1
beta0_black 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
beta0_pelagic 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0
beta0_pH 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta0_yellow 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1
beta1_black 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1
beta1_pelagic 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1
beta1_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta1_yellow 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1
beta2_black 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0
beta2_pelagic 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0
beta2_pH 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
beta2_yellow 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1
beta3_black 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0
beta3_pH 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta3_yellow 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1
mu_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_black 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.124 0.076 -0.265 -0.126 0.034
mu_bc_H[2] -0.114 0.039 -0.185 -0.117 -0.033
mu_bc_H[3] -0.454 0.067 -0.577 -0.454 -0.322
mu_bc_H[4] -1.012 0.193 -1.406 -1.008 -0.642
mu_bc_H[5] 0.761 0.860 -0.256 0.618 2.755
mu_bc_H[6] -2.272 0.322 -2.878 -2.286 -1.622
mu_bc_H[7] -0.457 0.112 -0.684 -0.452 -0.248
mu_bc_H[8] 0.197 0.343 -0.347 0.166 1.002
mu_bc_H[9] -0.322 0.135 -0.587 -0.320 -0.065
mu_bc_H[10] -0.114 0.067 -0.245 -0.115 0.023
mu_bc_H[11] -0.121 0.040 -0.199 -0.121 -0.039
mu_bc_H[12] -0.249 0.106 -0.472 -0.246 -0.051
mu_bc_H[13] -0.139 0.079 -0.298 -0.140 0.021
mu_bc_H[14] -0.288 0.105 -0.506 -0.285 -0.097
mu_bc_H[15] -0.348 0.054 -0.454 -0.348 -0.241
mu_bc_H[16] -0.371 0.380 -1.018 -0.398 0.490
mu_bc_R[1] 1.408 0.153 1.120 1.407 1.703
mu_bc_R[2] 1.497 0.089 1.321 1.498 1.674
mu_bc_R[3] 1.477 0.142 1.195 1.482 1.749
mu_bc_R[4] 1.024 0.199 0.605 1.036 1.373
mu_bc_R[5] 1.349 0.456 0.432 1.352 2.219
mu_bc_R[6] -1.421 0.432 -2.284 -1.412 -0.580
mu_bc_R[7] 0.296 0.197 -0.092 0.295 0.671
mu_bc_R[8] 0.554 0.197 0.164 0.553 0.941
mu_bc_R[9] 0.433 0.193 0.024 0.448 0.768
mu_bc_R[10] 1.345 0.127 1.093 1.348 1.596
mu_bc_R[11] 1.174 0.078 1.020 1.174 1.324
mu_bc_R[12] 0.936 0.200 0.532 0.935 1.325
mu_bc_R[13] 1.080 0.109 0.870 1.079 1.301
mu_bc_R[14] 1.011 0.149 0.722 1.007 1.314
mu_bc_R[15] 0.917 0.098 0.723 0.916 1.110
mu_bc_R[16] 1.233 0.120 0.991 1.234 1.459
tau_pH[1] 1.754 0.835 0.237 1.950 3.014
tau_pH[2] 2.296 0.847 0.683 2.503 3.566
tau_pH[3] 2.997 0.447 2.190 2.977 3.919
tau_pH[4] 8.734 5.357 0.481 8.730 19.891
tau_pH[5] 1.323 1.289 0.108 0.527 3.869
beta0_pH[1,1] 0.753 0.705 -0.381 0.612 2.703
beta0_pH[2,1] 0.502 2.418 -3.483 1.442 4.143
beta0_pH[3,1] 2.023 0.647 1.161 1.842 3.634
beta0_pH[4,1] 2.202 0.647 1.333 2.049 3.917
beta0_pH[5,1] 0.109 0.572 -0.982 0.092 1.126
beta0_pH[6,1] 0.566 0.463 -0.526 0.630 1.391
beta0_pH[7,1] 0.674 0.293 -0.145 0.700 1.167
beta0_pH[8,1] 0.011 0.576 -0.811 -0.154 1.282
beta0_pH[9,1] 0.339 0.594 -0.833 0.595 1.116
beta0_pH[10,1] 0.667 0.295 0.069 0.699 1.156
beta0_pH[11,1] 0.793 1.058 -0.265 0.465 4.314
beta0_pH[12,1] 0.868 0.481 0.133 0.793 2.124
beta0_pH[13,1] 0.749 1.127 -0.666 0.463 4.511
beta0_pH[14,1] 0.473 0.822 -0.629 0.407 2.536
beta0_pH[15,1] 0.606 1.204 -0.742 0.214 3.996
beta0_pH[16,1] 1.877 1.087 -0.239 1.997 3.599
beta0_pH[1,2] 1.988 1.455 -2.138 2.518 3.053
beta0_pH[2,2] 2.129 1.143 -0.147 2.725 3.145
beta0_pH[3,2] 2.194 0.753 0.533 2.439 3.193
beta0_pH[4,2] 2.597 0.278 1.898 2.661 2.989
beta0_pH[5,2] 4.120 1.243 2.235 3.951 6.903
beta0_pH[6,2] 2.901 0.454 2.162 2.933 3.569
beta0_pH[7,2] 1.952 0.244 1.442 1.951 2.453
beta0_pH[8,2] 2.668 0.601 0.792 2.795 3.225
beta0_pH[9,2] 3.007 0.624 1.720 3.190 3.942
beta0_pH[10,2] 3.621 0.392 2.609 3.678 4.225
beta0_pH[11,2] -3.963 1.196 -5.073 -4.560 -0.938
beta0_pH[12,2] -4.615 0.477 -5.554 -4.625 -3.629
beta0_pH[13,2] -4.471 0.438 -5.243 -4.508 -3.523
beta0_pH[14,2] -5.485 0.631 -7.086 -5.368 -4.537
beta0_pH[15,2] -3.597 1.556 -4.704 -4.151 0.817
beta0_pH[16,2] -4.547 0.517 -5.392 -4.606 -3.287
beta0_pH[1,3] 1.396 0.214 0.964 1.401 1.797
beta0_pH[2,3] 1.769 0.342 1.034 1.779 2.333
beta0_pH[3,3] 1.781 0.377 1.000 1.772 2.556
beta0_pH[4,3] 2.020 0.606 0.946 1.918 3.071
beta0_pH[5,3] 1.336 2.049 -2.553 1.117 5.947
beta0_pH[6,3] -1.606 0.892 -2.647 -1.798 0.780
beta0_pH[7,3] -1.674 0.929 -3.442 -1.734 0.456
beta0_pH[8,3] 0.285 0.172 -0.055 0.281 0.620
beta0_pH[9,3] -0.017 0.326 -0.670 -0.012 0.599
beta0_pH[10,3] 0.784 0.300 0.138 0.804 1.309
beta0_pH[11,4] 1.371 1.019 -0.122 1.473 2.730
beta0_pH[12,4] -0.597 1.731 -2.750 -0.359 3.060
beta0_pH[13,4] 0.414 0.912 -1.075 0.242 2.211
beta0_pH[14,4] -0.145 0.848 -2.177 -0.187 1.705
beta0_pH[15,4] 0.304 0.713 -0.742 0.264 1.913
beta0_pH[16,4] -0.122 0.463 -0.793 -0.226 0.983
beta0_pH[11,5] 0.610 0.998 -0.561 0.082 2.763
beta0_pH[12,5] -0.791 1.891 -3.005 -1.335 2.726
beta0_pH[13,5] 0.745 1.010 -0.615 0.651 2.666
beta0_pH[14,5] 0.280 1.126 -1.183 0.177 2.758
beta0_pH[15,5] 0.600 1.473 -1.741 0.764 3.290
beta0_pH[16,5] 0.474 1.305 -1.084 0.103 2.948
beta1_pH[1,1] 2.656 0.924 0.444 2.650 4.414
beta1_pH[2,1] 3.851 3.299 0.035 2.206 10.207
beta1_pH[3,1] 3.102 3.302 0.031 2.261 14.810
beta1_pH[4,1] 2.528 1.284 0.028 2.519 5.502
beta1_pH[5,1] 1.423 0.621 0.138 1.460 2.596
beta1_pH[6,1] 1.801 1.072 0.201 1.568 4.444
beta1_pH[7,1] 4.420 6.056 0.245 1.426 18.861
beta1_pH[8,1] 2.568 1.656 0.054 2.249 6.032
beta1_pH[9,1] 1.528 0.696 0.115 1.577 2.686
beta1_pH[10,1] 1.608 0.647 0.082 1.595 2.620
beta1_pH[11,1] 5.207 2.357 0.861 4.911 10.624
beta1_pH[12,1] 2.553 0.533 1.344 2.603 3.491
beta1_pH[13,1] 3.960 1.541 0.528 4.204 6.361
beta1_pH[14,1] 10.626 3.772 3.733 10.364 19.795
beta1_pH[15,1] 6.512 1.959 1.513 6.770 9.399
beta1_pH[16,1] 7.752 3.748 1.371 7.801 14.252
beta1_pH[1,2] 1.425 1.444 0.000 0.999 5.079
beta1_pH[2,2] 1.818 1.537 0.001 1.536 5.650
beta1_pH[3,2] 1.214 0.759 0.002 1.172 2.748
beta1_pH[4,2] 1.426 1.530 0.000 0.940 5.531
beta1_pH[5,2] 1.333 2.677 0.000 0.086 11.517
beta1_pH[6,2] 0.799 1.134 0.000 0.334 2.992
beta1_pH[7,2] 0.936 1.695 0.000 0.067 6.343
beta1_pH[8,2] 0.477 0.896 0.000 0.034 3.134
beta1_pH[9,2] 0.677 1.015 0.000 0.107 2.370
beta1_pH[10,2] 1.325 4.116 0.000 0.063 10.614
beta1_pH[11,2] 5.828 1.369 1.789 6.450 7.001
beta1_pH[12,2] 6.419 0.596 5.291 6.381 7.639
beta1_pH[13,2] 6.918 0.479 5.913 6.940 7.815
beta1_pH[14,2] 7.401 0.658 6.384 7.312 9.025
beta1_pH[15,2] 6.751 0.976 4.713 6.727 9.456
beta1_pH[16,2] 7.276 0.537 5.880 7.336 8.118
beta1_pH[1,3] 1.799 0.359 1.137 1.794 2.513
beta1_pH[2,3] 0.771 0.705 0.034 0.731 1.566
beta1_pH[3,3] 0.979 0.487 0.082 0.950 1.805
beta1_pH[4,3] 1.078 0.614 0.022 1.101 2.384
beta1_pH[5,3] 3.590 2.211 1.250 3.017 9.293
beta1_pH[6,3] 3.123 2.158 1.197 2.794 7.010
beta1_pH[7,3] 2.535 0.899 0.549 2.580 4.309
beta1_pH[8,3] 2.741 0.318 2.132 2.737 3.363
beta1_pH[9,3] 2.093 0.379 1.356 2.084 2.845
beta1_pH[10,3] 2.589 0.372 1.939 2.564 3.387
beta1_pH[11,4] 2.580 1.739 0.158 2.231 5.847
beta1_pH[12,4] 3.627 1.626 0.219 3.476 5.775
beta1_pH[13,4] 2.540 1.895 0.216 2.328 8.946
beta1_pH[14,4] 2.669 0.915 0.401 2.673 4.501
beta1_pH[15,4] 3.852 1.785 0.834 3.266 7.927
beta1_pH[16,4] 3.135 1.256 1.006 2.904 6.814
beta1_pH[11,5] 8.881 10.306 0.388 3.556 35.131
beta1_pH[12,5] 4.224 3.192 0.001 3.782 12.044
beta1_pH[13,5] 2.916 2.097 0.000 2.994 7.409
beta1_pH[14,5] 3.739 5.089 0.000 1.990 20.321
beta1_pH[15,5] 2.179 1.781 0.000 1.722 6.419
beta1_pH[16,5] 2.492 2.185 0.000 2.187 7.803
beta2_pH[1,1] 1.253 1.340 0.220 0.731 3.614
beta2_pH[2,1] 1.001 1.898 0.039 0.480 6.038
beta2_pH[3,1] 0.308 3.220 -7.761 0.442 6.717
beta2_pH[4,1] 0.962 2.718 -3.537 0.452 7.767
beta2_pH[5,1] 3.013 4.217 0.105 1.311 14.212
beta2_pH[6,1] 2.252 3.088 0.128 0.924 11.228
beta2_pH[7,1] -0.441 4.984 -12.384 0.316 9.914
beta2_pH[8,1] 1.293 3.959 -6.949 0.482 11.797
beta2_pH[9,1] 1.455 5.268 -7.125 0.455 15.069
beta2_pH[10,1] 1.739 2.251 0.196 0.801 9.140
beta2_pH[11,1] 1.353 2.397 0.124 0.329 8.372
beta2_pH[12,1] 1.786 2.327 0.363 0.997 8.533
beta2_pH[13,1] 1.202 2.656 0.104 0.307 10.428
beta2_pH[14,1] 0.755 1.706 0.239 0.341 5.509
beta2_pH[15,1] 0.759 1.584 0.037 0.232 6.323
beta2_pH[16,1] 0.117 2.362 -6.339 0.354 5.018
beta2_pH[1,2] 2.651 6.111 -10.496 2.421 15.516
beta2_pH[2,2] 0.167 6.334 -13.147 -0.663 13.612
beta2_pH[3,2] -1.063 5.827 -13.995 -1.308 7.332
beta2_pH[4,2] -4.475 4.867 -14.667 -3.593 4.453
beta2_pH[5,2] -0.201 6.375 -14.201 -0.057 12.770
beta2_pH[6,2] -2.353 6.075 -15.550 -2.298 10.670
beta2_pH[7,2] -2.169 5.945 -14.661 -2.234 11.021
beta2_pH[8,2] -0.102 5.550 -11.926 0.314 10.452
beta2_pH[9,2] -2.484 6.277 -16.078 -2.620 11.621
beta2_pH[10,2] -1.958 6.400 -15.134 -2.132 11.357
beta2_pH[11,2] -7.040 3.840 -16.353 -6.535 -1.307
beta2_pH[12,2] -4.098 3.176 -12.245 -3.380 -0.627
beta2_pH[13,2] -4.421 2.854 -11.690 -3.508 -1.425
beta2_pH[14,2] -5.137 3.171 -13.835 -4.211 -1.885
beta2_pH[15,2] -6.294 3.293 -14.397 -5.875 -0.154
beta2_pH[16,2] -7.745 3.378 -16.005 -7.134 -3.111
beta2_pH[1,3] 3.335 2.434 0.506 3.019 9.643
beta2_pH[2,3] 3.491 4.577 -5.247 2.717 14.505
beta2_pH[3,3] 0.265 6.150 -12.489 1.000 12.467
beta2_pH[4,3] 2.868 5.071 -8.794 2.525 13.947
beta2_pH[5,3] 5.610 4.340 -1.790 5.190 15.894
beta2_pH[6,3] 6.243 3.784 0.834 5.644 15.658
beta2_pH[7,3] 5.995 4.019 0.654 5.338 16.403
beta2_pH[8,3] 7.918 4.127 2.470 6.919 18.554
beta2_pH[9,3] 6.201 3.689 1.446 5.389 15.574
beta2_pH[10,3] 5.589 3.896 0.643 4.927 15.429
beta2_pH[11,4] 1.461 6.433 -15.005 2.218 13.280
beta2_pH[12,4] 1.372 5.350 -7.599 -0.758 15.164
beta2_pH[13,4] 2.352 3.661 -3.455 1.337 11.741
beta2_pH[14,4] -0.350 6.987 -12.560 -1.197 15.354
beta2_pH[15,4] -1.678 4.364 -14.590 0.078 2.912
beta2_pH[16,4] 5.537 4.616 0.155 4.562 16.839
beta2_pH[11,5] -4.015 3.159 -11.425 -3.493 -0.455
beta2_pH[12,5] -4.523 3.017 -10.046 -4.910 -0.114
beta2_pH[13,5] -4.078 2.827 -10.628 -3.889 0.364
beta2_pH[14,5] -4.656 3.772 -14.384 -4.221 0.684
beta2_pH[15,5] -4.392 3.053 -12.018 -4.143 -0.479
beta2_pH[16,5] -3.733 3.240 -10.072 -3.579 1.769
beta3_pH[1,1] 34.912 2.926 26.893 35.421 39.933
beta3_pH[2,1] 30.311 6.865 19.004 32.815 44.441
beta3_pH[3,1] 33.264 7.066 18.505 35.387 42.921
beta3_pH[4,1] 36.606 4.966 21.531 36.531 44.362
beta3_pH[5,1] 31.861 4.523 25.550 31.724 43.153
beta3_pH[6,1] 37.731 7.652 19.431 41.347 45.540
beta3_pH[7,1] 33.650 9.812 18.839 36.572 45.569
beta3_pH[8,1] 35.446 7.513 18.438 38.519 44.702
beta3_pH[9,1] 29.152 7.320 18.214 30.627 41.758
beta3_pH[10,1] 31.535 2.914 25.712 32.285 35.816
beta3_pH[11,1] 33.571 5.281 22.932 33.929 44.305
beta3_pH[12,1] 30.753 0.985 28.694 30.798 33.200
beta3_pH[13,1] 34.891 4.808 26.175 36.120 42.029
beta3_pH[14,1] 38.820 3.016 31.682 39.766 42.378
beta3_pH[15,1] 39.105 3.985 28.688 39.081 45.634
beta3_pH[16,1] 38.376 8.763 18.754 42.657 45.850
beta3_pH[1,2] 34.801 7.921 19.026 39.490 44.415
beta3_pH[2,2] 28.884 3.864 20.185 29.049 38.409
beta3_pH[3,2] 34.703 8.063 19.056 40.022 43.454
beta3_pH[4,2] 29.871 9.046 18.625 25.989 45.187
beta3_pH[5,2] 31.659 8.097 18.566 31.388 45.363
beta3_pH[6,2] 33.397 6.501 19.161 35.052 44.842
beta3_pH[7,2] 29.574 7.933 18.521 28.056 44.878
beta3_pH[8,2] 31.115 7.858 18.702 30.183 45.383
beta3_pH[9,2] 36.724 8.782 19.256 40.745 45.697
beta3_pH[10,2] 33.509 7.477 19.352 32.745 45.306
beta3_pH[11,2] 43.112 0.563 41.708 43.293 43.715
beta3_pH[12,2] 43.138 0.268 42.459 43.153 43.648
beta3_pH[13,2] 43.828 0.165 43.381 43.859 44.073
beta3_pH[14,2] 43.315 0.207 43.031 43.286 43.830
beta3_pH[15,2] 40.749 6.921 19.502 43.353 43.748
beta3_pH[16,2] 43.476 0.177 43.143 43.472 43.810
beta3_pH[1,3] 40.061 0.712 38.462 40.088 41.346
beta3_pH[2,3] 34.484 6.633 19.374 34.312 45.593
beta3_pH[3,3] 34.813 6.520 20.134 33.113 43.228
beta3_pH[4,3] 26.386 5.825 18.223 26.245 42.361
beta3_pH[5,3] 27.542 6.633 18.369 26.709 43.175
beta3_pH[6,3] 31.777 3.066 24.050 32.499 35.511
beta3_pH[7,3] 26.515 3.041 20.334 26.048 31.411
beta3_pH[8,3] 41.496 0.215 41.114 41.487 41.904
beta3_pH[9,3] 33.761 0.406 33.023 33.782 34.636
beta3_pH[10,3] 36.062 0.513 34.809 36.093 36.826
beta3_pH[11,4] 35.971 5.891 28.379 35.523 45.585
beta3_pH[12,4] 37.299 5.987 28.218 41.294 43.062
beta3_pH[13,4] 32.367 3.670 29.742 30.928 44.633
beta3_pH[14,4] 37.307 5.562 28.896 40.978 42.491
beta3_pH[15,4] 37.741 4.528 28.710 40.266 43.019
beta3_pH[16,4] 29.937 1.079 28.351 29.596 32.664
beta3_pH[11,5] 34.560 4.889 28.241 34.364 41.333
beta3_pH[12,5] 39.659 2.953 33.317 39.318 45.237
beta3_pH[13,5] 41.277 1.897 37.215 40.887 45.637
beta3_pH[14,5] 38.068 3.633 28.652 39.260 43.796
beta3_pH[15,5] 38.432 4.432 28.638 39.417 43.705
beta3_pH[16,5] 33.297 4.913 28.189 30.528 43.042
beta0_pelagic[1] 2.006 0.295 1.171 2.076 2.379
beta0_pelagic[2] 1.008 0.428 0.212 1.019 1.631
beta0_pelagic[3] 0.511 0.267 -0.057 0.528 0.965
beta0_pelagic[4] 0.678 0.283 0.131 0.692 1.148
beta0_pelagic[5] 0.949 1.030 -2.189 1.318 1.694
beta0_pelagic[6] 1.584 0.143 1.298 1.590 1.855
beta0_pelagic[7] 1.551 0.130 1.303 1.549 1.801
beta0_pelagic[8] 1.860 0.135 1.580 1.869 2.105
beta0_pelagic[9] 2.277 0.543 1.076 2.527 2.881
beta0_pelagic[10] 2.560 0.131 2.290 2.565 2.804
beta0_pelagic[11] 0.334 0.181 -0.069 0.330 0.738
beta0_pelagic[12] 1.759 0.136 1.510 1.749 2.042
beta0_pelagic[13] 0.581 0.129 0.314 0.583 0.820
beta0_pelagic[14] 0.412 0.172 0.090 0.402 0.769
beta0_pelagic[15] -0.240 0.139 -0.504 -0.249 0.012
beta0_pelagic[16] 0.474 0.183 0.070 0.510 0.745
beta1_pelagic[1] 0.264 0.337 0.000 0.136 1.194
beta1_pelagic[2] 0.594 0.499 0.000 0.604 1.486
beta1_pelagic[3] 0.563 0.447 0.000 0.527 1.657
beta1_pelagic[4] 0.555 0.360 0.000 0.557 1.385
beta1_pelagic[5] 0.474 1.106 0.000 0.000 3.823
beta1_pelagic[6] 0.025 0.095 0.000 0.000 0.292
beta1_pelagic[7] 0.053 0.320 0.000 0.000 0.366
beta1_pelagic[8] 0.084 0.492 0.000 0.000 0.769
beta1_pelagic[9] 0.497 0.686 0.000 0.002 2.015
beta1_pelagic[10] 0.020 0.074 0.000 0.000 0.239
beta1_pelagic[11] 4.017 0.695 2.649 4.134 5.361
beta1_pelagic[12] 2.684 0.313 2.114 2.667 3.308
beta1_pelagic[13] 2.274 0.516 1.477 2.215 3.449
beta1_pelagic[14] 3.660 0.768 2.353 3.622 5.308
beta1_pelagic[15] 2.537 0.253 2.060 2.538 3.034
beta1_pelagic[16] 3.578 0.907 2.747 3.187 5.933
beta2_pelagic[1] -1.333 6.729 -16.091 0.016 10.402
beta2_pelagic[2] 2.794 5.293 -8.382 1.955 15.050
beta2_pelagic[3] 3.343 5.027 -6.772 2.446 15.204
beta2_pelagic[4] 3.835 3.632 0.048 3.254 13.513
beta2_pelagic[5] -1.108 5.582 -12.345 -1.577 11.226
beta2_pelagic[6] -0.138 6.103 -12.703 -0.334 13.160
beta2_pelagic[7] -0.303 5.507 -11.584 -0.621 12.418
beta2_pelagic[8] -0.830 5.744 -13.124 -0.977 11.323
beta2_pelagic[9] 0.373 4.919 -7.916 0.247 11.901
beta2_pelagic[10] -1.183 4.831 -11.882 -0.907 9.185
beta2_pelagic[11] 0.309 0.185 0.154 0.239 0.907
beta2_pelagic[12] 6.129 3.971 1.489 5.117 16.236
beta2_pelagic[13] 1.603 2.193 0.321 0.744 7.872
beta2_pelagic[14] 0.527 0.629 0.241 0.422 1.215
beta2_pelagic[15] 6.855 3.899 0.717 6.184 16.354
beta2_pelagic[16] 5.157 4.687 0.270 4.506 16.622
beta3_pelagic[1] 33.358 7.484 19.819 34.608 45.678
beta3_pelagic[2] 26.166 7.718 18.156 22.655 42.336
beta3_pelagic[3] 32.179 6.221 21.084 30.539 44.650
beta3_pelagic[4] 29.097 5.011 21.550 27.488 40.435
beta3_pelagic[5] 34.275 8.976 18.928 34.793 45.978
beta3_pelagic[6] 30.507 6.902 19.299 28.344 44.693
beta3_pelagic[7] 29.367 8.162 18.529 27.926 45.140
beta3_pelagic[8] 31.846 8.040 18.590 31.882 45.285
beta3_pelagic[9] 30.431 6.783 19.212 29.044 44.745
beta3_pelagic[10] 32.579 7.755 18.916 33.443 45.264
beta3_pelagic[11] 44.504 0.919 42.654 44.567 45.923
beta3_pelagic[12] 43.485 0.247 43.050 43.480 43.930
beta3_pelagic[13] 42.691 1.063 40.591 42.812 44.386
beta3_pelagic[14] 43.831 1.109 41.435 43.819 45.849
beta3_pelagic[15] 43.297 0.241 42.870 43.269 43.768
beta3_pelagic[16] 43.509 0.646 42.774 43.311 45.547
mu_beta0_pelagic[1] 1.018 0.580 -0.150 1.019 2.160
mu_beta0_pelagic[2] 1.779 0.450 0.621 1.828 2.472
mu_beta0_pelagic[3] 0.548 0.360 -0.197 0.552 1.246
tau_beta0_pelagic[1] 2.206 2.783 0.138 1.527 8.417
tau_beta0_pelagic[2] 3.389 2.986 0.219 2.629 11.427
tau_beta0_pelagic[3] 2.279 1.599 0.341 1.910 6.321
beta0_yellow[1] -0.532 0.199 -1.004 -0.506 -0.209
beta0_yellow[2] 0.415 0.247 -0.288 0.457 0.780
beta0_yellow[3] -0.323 0.230 -1.066 -0.299 0.024
beta0_yellow[4] 0.548 0.587 -0.963 0.789 1.212
beta0_yellow[5] -0.930 0.532 -1.918 -0.944 0.051
beta0_yellow[6] 0.238 0.204 -0.161 0.235 0.643
beta0_yellow[7] 0.998 0.224 0.397 1.026 1.340
beta0_yellow[8] 0.589 0.809 -2.119 0.907 1.269
beta0_yellow[9] -0.021 0.247 -0.480 -0.027 0.491
beta0_yellow[10] 0.243 0.145 -0.022 0.239 0.541
beta0_yellow[11] -0.529 0.543 -1.578 -0.307 0.145
beta0_yellow[12] -3.566 0.473 -4.463 -3.569 -2.666
beta0_yellow[13] -3.542 0.430 -4.374 -3.589 -2.701
beta0_yellow[14] -0.724 0.800 -2.872 -0.377 0.045
beta0_yellow[15] -2.166 0.590 -3.148 -2.171 -1.122
beta0_yellow[16] -1.458 0.636 -2.492 -1.594 -0.158
beta1_yellow[1] 0.502 0.651 0.000 0.370 1.813
beta1_yellow[2] 1.215 0.542 0.564 1.076 2.728
beta1_yellow[3] 0.670 0.288 0.013 0.650 1.417
beta1_yellow[4] 2.221 1.562 0.658 1.431 5.616
beta1_yellow[5] 1.932 1.484 0.007 2.304 4.352
beta1_yellow[6] 2.305 0.354 1.623 2.302 3.008
beta1_yellow[7] 3.772 2.855 0.000 3.302 10.115
beta1_yellow[8] 1.652 1.506 0.000 1.369 5.106
beta1_yellow[9] 1.442 0.367 0.746 1.447 2.113
beta1_yellow[10] 2.572 0.470 1.720 2.557 3.518
beta1_yellow[11] 1.458 0.912 0.101 1.278 3.920
beta1_yellow[12] 2.342 0.492 1.402 2.341 3.273
beta1_yellow[13] 2.730 0.430 1.861 2.768 3.502
beta1_yellow[14] 1.253 0.763 0.068 1.066 3.033
beta1_yellow[15] 1.544 0.524 0.548 1.560 2.528
beta1_yellow[16] 1.430 0.628 0.031 1.472 2.567
beta2_yellow[1] -2.538 4.214 -12.714 -1.662 5.741
beta2_yellow[2] -2.977 3.455 -12.527 -1.740 -0.094
beta2_yellow[3] -3.142 3.585 -12.572 -1.898 -0.109
beta2_yellow[4] -1.967 2.962 -10.122 -0.532 -0.047
beta2_yellow[5] -5.409 6.760 -18.979 -5.276 9.951
beta2_yellow[6] 6.265 4.534 1.119 4.972 17.867
beta2_yellow[7] -5.882 6.530 -19.418 -5.587 8.458
beta2_yellow[8] -1.566 7.748 -17.374 -1.628 14.225
beta2_yellow[9] 6.059 4.066 0.675 4.968 17.340
beta2_yellow[10] -7.754 5.044 -20.469 -6.682 -1.207
beta2_yellow[11] -2.789 2.892 -10.794 -2.038 -0.103
beta2_yellow[12] -4.500 3.185 -13.245 -3.609 -1.015
beta2_yellow[13] -4.204 2.800 -11.227 -3.406 -1.245
beta2_yellow[14] -3.631 3.378 -13.217 -2.805 -0.147
beta2_yellow[15] -3.862 3.030 -11.406 -3.161 -0.159
beta2_yellow[16] -4.182 3.525 -12.773 -3.450 -0.056
beta3_yellow[1] 28.169 7.472 18.357 26.610 44.863
beta3_yellow[2] 29.677 2.652 23.171 29.236 35.616
beta3_yellow[3] 34.028 3.709 28.553 33.262 43.955
beta3_yellow[4] 27.717 3.808 19.346 27.727 35.336
beta3_yellow[5] 33.062 4.715 20.369 33.415 44.165
beta3_yellow[6] 39.630 0.477 38.853 39.599 40.814
beta3_yellow[7] 22.997 6.766 18.663 20.330 44.270
beta3_yellow[8] 26.700 6.350 18.370 25.836 44.525
beta3_yellow[9] 37.772 1.175 36.383 37.608 42.162
beta3_yellow[10] 29.410 0.391 28.500 29.447 29.975
beta3_yellow[11] 37.122 6.982 28.364 33.921 45.831
beta3_yellow[12] 43.343 0.455 42.472 43.329 44.221
beta3_yellow[13] 44.831 0.421 43.923 44.913 45.536
beta3_yellow[14] 36.228 5.531 28.589 34.354 45.264
beta3_yellow[15] 43.424 3.549 33.449 44.896 45.915
beta3_yellow[16] 41.792 5.155 28.753 44.109 45.768
mu_beta0_yellow[1] 0.022 0.449 -0.838 0.011 0.978
mu_beta0_yellow[2] 0.176 0.407 -0.746 0.202 0.937
mu_beta0_yellow[3] -1.592 0.730 -2.842 -1.660 0.063
tau_beta0_yellow[1] 5.145 12.502 0.242 2.267 30.325
tau_beta0_yellow[2] 2.562 4.332 0.265 1.633 9.963
tau_beta0_yellow[3] 0.510 0.377 0.076 0.418 1.484
beta0_black[1] -0.072 0.148 -0.367 -0.067 0.213
beta0_black[2] 1.880 0.147 1.560 1.889 2.143
beta0_black[3] 1.285 0.149 0.956 1.292 1.555
beta0_black[4] 2.001 0.278 1.305 2.020 2.490
beta0_black[5] 1.633 1.608 -1.285 1.663 4.194
beta0_black[6] 1.657 1.545 -1.035 1.636 4.408
beta0_black[7] 1.652 1.517 -1.202 1.681 4.129
beta0_black[8] 1.281 0.234 0.819 1.286 1.719
beta0_black[9] 2.361 0.289 1.720 2.374 2.879
beta0_black[10] 1.468 0.135 1.205 1.467 1.731
beta0_black[11] 3.414 0.179 3.041 3.429 3.740
beta0_black[12] 4.468 0.196 4.068 4.473 4.831
beta0_black[13] -0.108 0.215 -0.556 -0.096 0.300
beta0_black[14] 2.136 0.433 1.019 2.212 2.786
beta0_black[15] 1.124 0.254 0.497 1.160 1.522
beta0_black[16] 4.031 0.407 2.929 4.145 4.521
beta2_black[1] 5.396 4.152 0.912 4.187 16.571
beta2_black[2] 1.552 7.229 -11.567 0.591 16.925
beta2_black[3] 0.372 6.053 -11.168 0.329 12.457
beta2_black[4] -2.173 2.289 -7.274 -1.642 1.662
beta2_black[5] -0.184 6.568 -13.615 -0.217 13.077
beta2_black[6] -0.383 6.516 -13.848 -0.503 13.040
beta2_black[7] -0.279 6.758 -14.256 -0.218 13.912
beta2_black[8] -0.528 6.666 -14.121 -0.696 13.546
beta2_black[9] -0.444 6.574 -13.451 -0.595 12.970
beta2_black[10] -0.089 6.590 -13.357 -0.335 14.110
beta2_black[11] -1.787 2.401 -7.985 -1.288 0.483
beta2_black[12] -2.637 2.597 -10.425 -1.724 -0.529
beta2_black[13] -2.301 2.444 -9.109 -1.469 -0.488
beta2_black[14] -1.522 2.155 -7.718 -0.831 -0.125
beta2_black[15] -1.296 3.666 -8.853 -1.169 9.099
beta2_black[16] -0.230 3.451 -7.353 -0.167 7.488
beta3_black[1] 41.810 1.092 40.101 41.983 43.021
beta3_black[2] 32.111 8.055 18.652 32.549 45.324
beta3_black[3] 31.655 8.141 18.742 31.157 45.291
beta3_black[4] 32.913 4.005 21.434 32.882 40.726
beta3_black[5] 32.073 8.150 18.833 31.989 45.227
beta3_black[6] 32.261 8.063 18.598 32.534 45.177
beta3_black[7] 31.991 8.167 18.697 31.721 45.424
beta3_black[8] 31.561 8.123 18.633 31.326 45.208
beta3_black[9] 32.157 8.158 18.738 32.070 45.244
beta3_black[10] 31.875 8.231 18.723 31.492 45.329
beta3_black[11] 34.736 4.625 28.384 33.758 44.836
beta3_black[12] 32.678 1.361 29.495 32.846 34.142
beta3_black[13] 39.299 0.662 37.807 39.364 40.437
beta3_black[14] 38.617 3.091 30.448 38.963 44.637
beta3_black[15] 37.044 5.062 28.580 37.009 45.475
beta3_black[16] 36.007 5.279 28.295 35.482 45.555
beta4_black[1] -0.257 0.184 -0.626 -0.256 0.090
beta4_black[2] 0.251 0.172 -0.092 0.251 0.590
beta4_black[3] -0.936 0.181 -1.290 -0.935 -0.574
beta4_black[4] 0.544 0.218 0.118 0.541 0.975
beta4_black[5] 0.280 2.454 -4.135 0.152 5.312
beta4_black[6] 0.202 2.539 -4.504 0.157 5.022
beta4_black[7] 0.250 2.607 -4.640 0.174 5.291
beta4_black[8] -0.714 0.365 -1.425 -0.701 0.014
beta4_black[9] 1.526 1.042 -0.066 1.371 3.973
beta4_black[10] 0.022 0.186 -0.343 0.026 0.382
beta4_black[11] -0.699 0.205 -1.101 -0.701 -0.303
beta4_black[12] 0.308 0.335 -0.326 0.298 0.972
beta4_black[13] -1.202 0.211 -1.611 -1.204 -0.793
beta4_black[14] -0.134 0.229 -0.572 -0.133 0.324
beta4_black[15] -0.889 0.202 -1.293 -0.885 -0.508
beta4_black[16] -0.594 0.226 -1.029 -0.591 -0.149
mu_beta0_black[1] 1.217 0.703 -0.276 1.237 2.483
mu_beta0_black[2] 1.638 0.676 0.207 1.663 2.891
mu_beta0_black[3] 2.306 0.874 0.417 2.333 3.959
tau_beta0_black[1] 1.105 0.940 0.092 0.841 3.682
tau_beta0_black[2] 4.628 14.005 0.077 2.019 20.203
tau_beta0_black[3] 0.312 0.200 0.053 0.270 0.812
beta0_dsr[11] -3.023 0.281 -3.534 -3.048 -2.476
beta0_dsr[12] 4.476 0.275 3.949 4.473 5.048
beta0_dsr[13] -1.960 0.726 -3.669 -1.751 -1.022
beta0_dsr[14] -4.480 0.470 -5.504 -4.465 -3.536
beta0_dsr[15] -2.467 0.291 -3.038 -2.492 -1.848
beta0_dsr[16] -3.190 0.346 -3.887 -3.190 -2.510
beta1_dsr[11] 4.907 0.302 4.321 4.921 5.481
beta1_dsr[12] 5.998 3.192 2.415 5.302 13.811
beta1_dsr[13] 3.574 0.945 2.466 3.221 5.896
beta1_dsr[14] 7.118 0.495 6.142 7.114 8.151
beta1_dsr[15] 3.647 0.288 3.092 3.647 4.197
beta1_dsr[16] 5.966 0.361 5.261 5.957 6.681
beta2_dsr[11] -9.894 4.514 -23.726 -8.372 -5.135
beta2_dsr[12] -8.438 4.404 -19.143 -7.782 -2.164
beta2_dsr[13] -3.773 3.315 -11.112 -3.226 -0.252
beta2_dsr[14] -7.065 3.621 -17.199 -6.475 -2.510
beta2_dsr[15] -8.235 3.613 -16.817 -7.347 -3.303
beta2_dsr[16] -9.654 4.037 -19.980 -8.490 -4.678
beta3_dsr[11] 43.487 0.161 43.201 43.482 43.791
beta3_dsr[12] 34.013 0.681 32.179 34.155 34.823
beta3_dsr[13] 43.347 0.589 42.131 43.236 44.873
beta3_dsr[14] 43.277 0.158 43.074 43.242 43.740
beta3_dsr[15] 43.471 0.194 43.145 43.461 43.841
beta3_dsr[16] 43.445 0.172 43.150 43.432 43.791
beta4_dsr[11] 0.657 0.207 0.256 0.653 1.073
beta4_dsr[12] 0.334 0.468 -0.597 0.326 1.276
beta4_dsr[13] -0.088 0.215 -0.492 -0.087 0.333
beta4_dsr[14] 0.204 0.246 -0.293 0.207 0.673
beta4_dsr[15] 1.014 0.217 0.596 1.014 1.445
beta4_dsr[16] 0.197 0.222 -0.241 0.199 0.644
beta0_slope[11] -2.035 0.161 -2.352 -2.041 -1.721
beta0_slope[12] -4.672 0.272 -5.235 -4.664 -4.168
beta0_slope[13] -1.538 0.298 -2.307 -1.468 -1.132
beta0_slope[14] -2.695 0.197 -3.082 -2.691 -2.324
beta0_slope[15] -1.691 0.159 -1.977 -1.699 -1.361
beta0_slope[16] -2.760 0.163 -3.056 -2.765 -2.445
beta1_slope[11] 4.430 0.324 3.805 4.430 5.041
beta1_slope[12] 4.737 0.540 3.708 4.734 5.799
beta1_slope[13] 2.936 0.791 2.032 2.701 5.187
beta1_slope[14] 6.057 0.836 4.752 5.931 8.025
beta1_slope[15] 2.069 0.298 1.475 2.070 2.674
beta1_slope[16] 5.286 0.387 4.515 5.286 6.061
beta2_slope[11] 6.651 3.825 2.018 6.428 14.986
beta2_slope[12] 6.031 4.480 1.374 4.661 17.882
beta2_slope[13] 3.719 2.815 0.229 2.744 7.951
beta2_slope[14] 1.621 1.065 0.776 1.384 4.574
beta2_slope[15] 4.945 3.890 1.523 3.267 15.826
beta2_slope[16] 6.864 4.306 2.159 5.906 17.728
beta3_slope[11] 43.477 0.161 43.169 43.480 43.790
beta3_slope[12] 43.372 0.317 42.732 43.350 43.986
beta3_slope[13] 43.533 0.612 42.184 43.528 44.963
beta3_slope[14] 44.546 0.419 43.733 44.559 45.274
beta3_slope[15] 43.675 0.273 43.191 43.676 44.229
beta3_slope[16] 43.489 0.168 43.189 43.479 43.832
beta4_slope[11] -0.437 0.205 -0.838 -0.435 -0.036
beta4_slope[12] -1.190 0.660 -2.741 -1.109 -0.176
beta4_slope[13] 0.195 0.212 -0.207 0.187 0.623
beta4_slope[14] -0.083 0.245 -0.548 -0.094 0.396
beta4_slope[15] -0.210 0.205 -0.616 -0.209 0.178
beta4_slope[16] -0.145 0.221 -0.594 -0.141 0.294
sigma_H[1] 0.210 0.055 0.112 0.208 0.326
sigma_H[2] 0.174 0.030 0.120 0.172 0.240
sigma_H[3] 0.197 0.044 0.122 0.194 0.292
sigma_H[4] 0.410 0.077 0.285 0.403 0.595
sigma_H[5] 0.972 0.219 0.580 0.960 1.433
sigma_H[6] 0.404 0.210 0.028 0.390 0.851
sigma_H[7] 0.301 0.061 0.209 0.294 0.445
sigma_H[8] 0.436 0.107 0.280 0.419 0.683
sigma_H[9] 0.494 0.115 0.319 0.479 0.754
sigma_H[10] 0.218 0.043 0.147 0.213 0.317
sigma_H[11] 0.277 0.047 0.200 0.273 0.381
sigma_H[12] 0.446 0.166 0.212 0.428 0.776
sigma_H[13] 0.212 0.039 0.145 0.209 0.296
sigma_H[14] 0.495 0.095 0.330 0.489 0.696
sigma_H[15] 0.253 0.041 0.185 0.249 0.345
sigma_H[16] 0.228 0.045 0.153 0.224 0.325
lambda_H[1] 3.148 3.958 0.172 1.856 13.879
lambda_H[2] 8.499 7.787 0.920 6.297 28.619
lambda_H[3] 6.420 8.756 0.280 3.412 30.261
lambda_H[4] 0.007 0.005 0.001 0.006 0.018
lambda_H[5] 3.006 6.897 0.022 0.682 22.919
lambda_H[6] 9.195 16.104 0.010 2.455 59.589
lambda_H[7] 0.014 0.010 0.002 0.012 0.040
lambda_H[8] 7.935 10.774 0.001 3.717 41.784
lambda_H[9] 0.017 0.012 0.003 0.015 0.049
lambda_H[10] 0.294 0.436 0.034 0.200 1.129
lambda_H[11] 0.285 0.473 0.015 0.150 1.260
lambda_H[12] 5.166 6.521 0.203 3.006 22.759
lambda_H[13] 3.283 2.969 0.216 2.500 10.672
lambda_H[14] 3.603 4.198 0.269 2.275 15.452
lambda_H[15] 0.034 0.124 0.003 0.019 0.134
lambda_H[16] 2.108 3.158 0.117 1.228 9.119
mu_lambda_H[1] 4.396 1.926 1.286 4.264 8.607
mu_lambda_H[2] 3.780 1.956 0.569 3.595 7.802
mu_lambda_H[3] 3.617 1.854 0.865 3.312 7.951
sigma_lambda_H[1] 8.658 4.308 2.143 8.017 18.155
sigma_lambda_H[2] 8.393 4.768 0.984 7.754 18.475
sigma_lambda_H[3] 6.242 3.799 1.094 5.456 15.601
beta_H[1,1] 6.908 1.073 4.473 7.087 8.525
beta_H[2,1] 9.885 0.496 8.822 9.917 10.770
beta_H[3,1] 8.023 0.762 6.263 8.120 9.282
beta_H[4,1] 9.766 7.691 -5.285 9.747 24.565
beta_H[5,1] 0.151 2.573 -5.280 0.317 5.053
beta_H[6,1] 3.745 3.516 -5.856 4.975 7.465
beta_H[7,1] 1.039 5.704 -11.093 1.524 10.916
beta_H[8,1] 7.101 16.090 -2.495 1.560 57.707
beta_H[9,1] 13.407 5.610 2.770 13.258 24.505
beta_H[10,1] 7.107 1.731 3.561 7.176 10.468
beta_H[11,1] 5.633 3.147 -1.733 6.272 10.003
beta_H[12,1] 2.617 1.040 0.897 2.544 4.902
beta_H[13,1] 9.036 0.968 7.095 9.122 10.540
beta_H[14,1] 2.213 0.979 0.317 2.203 4.163
beta_H[15,1] -5.371 4.003 -12.601 -5.679 3.341
beta_H[16,1] 3.012 1.786 -0.408 3.022 6.809
beta_H[1,2] 7.898 0.250 7.375 7.906 8.372
beta_H[2,2] 10.041 0.134 9.787 10.039 10.306
beta_H[3,2] 8.964 0.193 8.582 8.962 9.347
beta_H[4,2] 3.395 1.475 0.602 3.370 6.441
beta_H[5,2] 1.997 0.996 0.005 2.024 3.859
beta_H[6,2] 6.008 0.988 3.582 6.195 7.493
beta_H[7,2] 2.462 1.103 0.532 2.409 4.798
beta_H[8,2] 1.689 3.789 -9.574 3.053 4.282
beta_H[9,2] 3.169 1.096 1.114 3.150 5.421
beta_H[10,2] 8.166 0.353 7.426 8.187 8.802
beta_H[11,2] 9.652 0.568 8.801 9.535 10.989
beta_H[12,2] 3.942 0.361 3.249 3.930 4.676
beta_H[13,2] 9.130 0.257 8.681 9.118 9.631
beta_H[14,2] 4.011 0.346 3.350 4.007 4.705
beta_H[15,2] 11.232 0.711 9.728 11.271 12.515
beta_H[16,2] 4.767 0.779 3.210 4.794 6.269
beta_H[1,3] 8.473 0.247 8.036 8.464 9.004
beta_H[2,3] 10.094 0.113 9.885 10.091 10.322
beta_H[3,3] 9.650 0.160 9.342 9.645 9.984
beta_H[4,3] -2.260 0.905 -4.016 -2.280 -0.472
beta_H[5,3] 4.021 0.656 2.744 4.025 5.330
beta_H[6,3] 7.987 1.099 6.549 7.637 10.577
beta_H[7,3] -2.583 0.740 -4.063 -2.569 -1.129
beta_H[8,3] 5.935 1.761 4.670 5.290 11.172
beta_H[9,3] -2.321 0.758 -3.830 -2.300 -0.833
beta_H[10,3] 8.764 0.285 8.217 8.758 9.341
beta_H[11,3] 8.604 0.267 8.027 8.628 9.084
beta_H[12,3] 5.269 0.313 4.529 5.306 5.788
beta_H[13,3] 8.858 0.195 8.475 8.858 9.250
beta_H[14,3] 5.706 0.272 5.128 5.711 6.217
beta_H[15,3] 10.434 0.329 9.806 10.427 11.094
beta_H[16,3] 6.798 0.471 5.752 6.846 7.623
beta_H[1,4] 8.267 0.188 7.846 8.279 8.592
beta_H[2,4] 10.171 0.112 9.941 10.176 10.371
beta_H[3,4] 10.152 0.157 9.817 10.166 10.427
beta_H[4,4] 11.728 0.446 10.773 11.740 12.546
beta_H[5,4] 5.762 0.838 4.465 5.643 7.652
beta_H[6,4] 7.417 0.826 5.257 7.663 8.450
beta_H[7,4] 8.205 0.354 7.510 8.204 8.911
beta_H[8,4] 6.475 0.678 4.456 6.683 7.131
beta_H[9,4] 7.113 0.451 6.248 7.111 7.991
beta_H[10,4] 7.746 0.239 7.289 7.741 8.229
beta_H[11,4] 9.320 0.203 8.917 9.318 9.717
beta_H[12,4] 7.120 0.205 6.721 7.117 7.531
beta_H[13,4] 9.020 0.139 8.742 9.020 9.296
beta_H[14,4] 7.670 0.216 7.258 7.666 8.103
beta_H[15,4] 9.430 0.240 8.954 9.433 9.895
beta_H[16,4] 9.130 0.187 8.798 9.113 9.532
beta_H[1,5] 8.968 0.150 8.669 8.970 9.247
beta_H[2,5] 10.794 0.092 10.618 10.792 10.974
beta_H[3,5] 10.924 0.169 10.628 10.916 11.278
beta_H[4,5] 8.402 0.458 7.527 8.374 9.357
beta_H[5,5] 5.315 0.662 3.745 5.406 6.374
beta_H[6,5] 8.702 0.546 7.875 8.609 10.097
beta_H[7,5] 6.770 0.343 6.101 6.762 7.474
beta_H[8,5] 8.371 0.520 7.821 8.228 9.940
beta_H[9,5] 8.217 0.448 7.337 8.220 9.081
beta_H[10,5] 10.078 0.230 9.614 10.075 10.522
beta_H[11,5] 11.539 0.236 11.051 11.545 11.991
beta_H[12,5] 8.475 0.195 8.091 8.475 8.874
beta_H[13,5] 10.025 0.130 9.776 10.024 10.288
beta_H[14,5] 9.181 0.235 8.752 9.169 9.670
beta_H[15,5] 11.177 0.247 10.683 11.181 11.673
beta_H[16,5] 9.947 0.149 9.645 9.951 10.231
beta_H[1,6] 10.172 0.191 9.842 10.157 10.599
beta_H[2,6] 11.504 0.106 11.303 11.500 11.719
beta_H[3,6] 10.814 0.160 10.470 10.823 11.090
beta_H[4,6] 12.861 0.818 11.131 12.880 14.424
beta_H[5,6] 5.944 0.640 4.773 5.912 7.306
beta_H[6,6] 8.868 0.572 7.366 8.922 9.738
beta_H[7,6] 9.812 0.568 8.698 9.813 10.941
beta_H[8,6] 9.278 0.734 6.903 9.489 9.988
beta_H[9,6] 8.452 0.757 7.014 8.439 9.944
beta_H[10,6] 9.511 0.315 8.853 9.537 10.060
beta_H[11,6] 10.826 0.347 10.076 10.853 11.457
beta_H[12,6] 9.371 0.256 8.886 9.360 9.889
beta_H[13,6] 11.078 0.162 10.788 11.066 11.412
beta_H[14,6] 9.861 0.284 9.284 9.859 10.416
beta_H[15,6] 10.869 0.435 10.021 10.876 11.725
beta_H[16,6] 10.577 0.187 10.184 10.589 10.918
beta_H[1,7] 10.944 0.873 8.850 11.036 12.385
beta_H[2,7] 12.183 0.420 11.293 12.193 12.995
beta_H[3,7] 10.579 0.639 9.219 10.627 11.681
beta_H[4,7] 2.533 4.212 -5.196 2.404 11.304
beta_H[5,7] 6.526 2.041 3.022 6.379 11.232
beta_H[6,7] 9.335 2.143 4.775 9.409 14.122
beta_H[7,7] 10.712 2.863 5.155 10.743 16.275
beta_H[8,7] 11.909 3.128 9.274 11.029 22.286
beta_H[9,7] 4.428 3.836 -3.197 4.482 11.956
beta_H[10,7] 9.825 1.449 7.148 9.719 12.988
beta_H[11,7] 10.978 1.663 7.886 10.851 14.614
beta_H[12,7] 10.044 0.888 8.101 10.101 11.630
beta_H[13,7] 11.640 0.799 9.685 11.767 12.831
beta_H[14,7] 10.481 0.911 8.515 10.534 12.133
beta_H[15,7] 12.110 2.248 7.768 12.030 16.550
beta_H[16,7] 11.843 0.942 10.362 11.705 14.150
beta0_H[1] 8.964 13.162 -16.035 8.893 37.045
beta0_H[2] 10.695 6.388 -2.168 10.718 23.948
beta0_H[3] 10.210 10.038 -9.851 10.166 31.404
beta0_H[4] -0.431 175.455 -364.882 3.619 359.935
beta0_H[5] 5.278 29.554 -51.589 4.721 68.251
beta0_H[6] 7.121 41.615 -83.491 7.537 92.358
beta0_H[7] 5.558 127.158 -245.964 6.232 261.346
beta0_H[8] 6.334 138.640 -292.921 6.516 294.390
beta0_H[9] 3.288 116.236 -238.081 3.837 232.470
beta0_H[10] 8.643 32.422 -61.955 9.304 73.912
beta0_H[11] 10.393 43.027 -76.958 10.096 102.428
beta0_H[12] 6.644 10.157 -15.315 6.786 25.635
beta0_H[13] 9.540 11.179 -11.824 9.539 30.943
beta0_H[14] 7.047 10.717 -14.986 7.135 28.649
beta0_H[15] 8.294 101.366 -205.482 8.835 210.186
beta0_H[16] 8.402 15.349 -21.551 8.139 40.141